You just need to set up the routing function in the PI and configure a route command on your PC to get the PC to connect to the F16 thru the PI. Checking the Route between Interfaces checkbox on the PI's network screen enables the routing on the PI and a route command needs to be entered on the PC (assuming Windows) to get them to talk to each other. I would need the IP addresses of the two PI interfaces and the F16 to give you the correct command.

Before I get too far into it, I need to know how you are planning to set up. The way most do it is to use WIFI to communicate with the PI. The PI then controls the controllers thru its Ethernet connection IOW, the PI and the F16 are wired together and the both of them are monitored from the PC over WIFI. If that's the way you want it to work, let be know and we can cable it up and configure them properly and if not, then let me know the way you want it to work. BTW, awesome job on that controller box. It looks like a commercial unit. I am impressed.

The IP of the wired falcon needs to be on the same subnet of eth0 on the pi. I would not worry about wireless on the Falcon if that is how it is going to be hooked up but I do not have that option on mine. I have attached my settings if that will help you